A solver, like an integer linear programming solver, will find optimal solutions (or approximations, depending on what you ask for, and how long you give it to run).
Right. For some problems it’ll be optimal in execution time, for most it won’t be and you may be forced to let it approximate. But that’s usually still good enough.
Which is distinct from spending time trying to find an optimal solution, in the general case.
In general, using a general purpose solver won't be 'optimal in execution time'. (And in general, we have no clue what the optimal execution time for any NP hard or NP complete problem is, because then we'd also have solved P vs NP.)
For some problems it’ll be optimal in execution time, for most it won’t be and you may be forced to let it approximate. But that’s usually still good enough.
Yes, it depends on your problem and your application. For some problems, you can approximate well, and in some applications that's good. And in some other applications it's fine to occasionally not solve a problem at all.
Comments
A solver, like an integer linear programming solver, will find optimal solutions (or approximations, depending on what you ask for, and how long you give it to run).
Right. For some problems it’ll be optimal in execution time, for most it won’t be and you may be forced to let it approximate. But that’s usually still good enough.
Which is distinct from spending time trying to find an optimal solution, in the general case.
In general, using a general purpose solver won't be 'optimal in execution time'. (And in general, we have no clue what the optimal execution time for any NP hard or NP complete problem is, because then we'd also have solved P vs NP.)
Yes, it depends on your problem and your application. For some problems, you can approximate well, and in some applications that's good. And in some other applications it's fine to occasionally not solve a problem at all.